Saturday 21 June 2014 05.00 EDT
First published on Saturday 21 June 2014 05.00 EDT

One of the most tantalising lost works of literature is an epic poem by Homer called Margites, which, unlike the Odyssey and Iliad, has not survived and is known from a reference by Aristotle. So a cultural commentator seeking a neat historical contrast might be tempted to observe that, while Homer's Margites has vanished from culture, Marge's Homer never will owing to the vast existing digital archive of episodes of The Simpsons.

The opening act plays out on an almost dark stage, illuminated only by spasmodic flashlight and the flames of a campfire, around which huddle the survivors of a near-futuristic American catastrophe caused by the meltdown of nuclear power stations. This homeland Chernobyl has destroyed all electronic entertainment present and past, with the result that groups of survivors compete to recreate, through oral story-telling, favoured episodes of network TV shows such as The Simpsons.

Seven years on, in the second act, these broadcasting restorationists have organised into a primitive industry. Rival troupes of travelling players, with names such as The Prime-time Players, The Reruns and Richard's Couch, tour the scorched states, performing by candlelight reconstituted adventures of Homer and Marge and their children – though one group resurrects instead The West Wing, with its now novel concept of national government – and buying extra lines of remembered dialogue from locals.

But, in one of Washburn's smartest touches, these mocked-up comedies are just a show within a show, framed by recreated scenes of the domestic life destroyed by the apocalypse – including coming home from work, baths, food and wine – and reenactments of old TV ads for domestic necessities that now seem as unlikely as unicorns. As one character comments of these pastiche commercials: "It's that fine line between tantalisation and torture."

A further 75 years have passed before the final section, which consists entirely of a performance of "Mister Burns", a one-act opera (composed by Orlando Gough and Michael Henry) in which Bart Simpson has become a Perseus-like hero, seeking to save his country from the evil central character, in a narrative that resembles a Chinese-whispered version of the Simpsons episode "Cape Feare" (Season 5, Episode 2, 1993), mixed up with snatches of Gilbert and Sullivan operettas and early 21st-century pop songs, including Britney Spears' "Toxic."

As often happens to brilliantly original and provocative plays, Mr Burns has met critical hostility and mystification, although the main objection of detractors oddly serves to make what Washburn has written seem even more timely and apposite.

What fascinates me about these reactions is that Washburn stands accused of writing a play with a narrow frame of reference, although the American cartoon she invokes has been seen by hundreds of millions of viewers, rather than the average thousands who attend a new play at a small theatre. Drawing on some of the most popular images and stories of our time, the dramatist is paradoxically charged with a sort of elitism by reviewers who either don't recognise or don't respect her references. So, inadvertently, the reviews are raising the question that Mr Burns itself asks: what constitutes a common culture?

Judging which allusions are universal (or at least broadly recognisable) is a recurrent dilemma for all sections of the entertainment business. The concern that an audience "won't get it" is the most usual justification for cutting TV and radio scripts, fictional and journalistic alike. Such comments can reflect an assumption that the consumers are less educated than the producers, but it is also becoming harder to assess what people know. Tom Stoppard has said that classical and literary allusions that seemed easily recognisable when his plays Rosencrantzand Guildenstern Are Dead and Jumpers were premiered in the 60s and 70s often mystified theatre-goers at revivals decades later because of a shift in the definition of what it meant to be well educated.

The increased patchiness and shallowness of the collective cultural memory is one reason that Tudor history has become so popular, through the best-selling novels of CJ Sansom, Philippa Gregory and Hilary Mantel and the current blockbuster stage productions based on Mantel's Wolf Hall and Bring up the Bodies. Since Christianity ceased to be mainstream in Britain, the story of Henry VIII's uxoricides is one of the few narratives that a cross-section of society and generations could be expected to recognise. And Mike Poulton's theatrical adaptations of the Mantels also make canny use of one of the country's few other general points of reference – the comedy of geographical stereotype – with references to "Yorkshire" and "Stoke Newington" winning big and knowing laughs.

The critical reception for Mr Burns illustrates the increasing discrepancies in general knowledge. A teenager unfamiliar with theatre would find Mr Burns easily comprehensible; but, to a theatre critic who doesn't watch much TV, it seems impenetrable. However, at Turgenev's Fathers and Sons at the Donmar, another recent London opening, reviewers would be more at home than most couch potatoes. But, at these two performances, which section of which audience can be regarded as dumb or cultish?

Photograph: Tristram Kenton for the Guardian

In this piece, I am tempted to say that the most suitable word of praise for Mr Burns is "excellent". If you know The Simpsons, you will know why; if you don't, you won't. But the fact that there is a third subset of readers who may have learned the catchword of Homer Simpson's boss through seepage from children or grandchildren is a further validation of Washburn's theme and thesis.

Mr Burns subtly dramatises the process of cultural transmission in a mass media era. In Washburn's post-apocalyptic world, the works of Joseph Conrad, William Shakespeare and Tennessee Williams apparently survive only in episodes of The Simpsons punningly titled "Bart of Darkness" , "Much Apu about Nothing" and "A Streetcar Named Marge."

So, although the playwright says in a programme note that the choice of The Simpsons as the show-within-the-play was "a lightly made decision" and she might easily have gone for Friends instead, her play gains an extra layer of meaning from the fact that Matt Groening's cartoon series is itself a complex web of references to art of the past.

As its title acknowledges, the "Cape Feare" episode is mainly influenced by cinema, although the thriller Cape Fear exists in both a 1962 version directed by J Lee Thompson and a 1991 Martin Scorsese remake; a distinction discussed by the play's characters. But, as well as the quotations from those films, the script also samples Gilbert and Sullivan's The Mikado and HMS Pinafore. Some critics seem not to have appreciated that the Savoy operetta references in Mr Burns came via The Simpsons, rather than being a random artistic garnish on Washburn's stew, which again demonstrates how the reception of a show can be affected by what audiences know.

During the performance I saw at the Almeida, for example, there were two varieties of laughter: a communal guffaw at jokes that arise from the context of the play and a smaller giggle of recognition at the Simpsons references or Madonna or Chris Isaak lyrics. The reaction when a portrait of President Clinton is revealed on a wall of the set seemed to split between liberal theatregoers rippling with pleasure at the politician's image and those clocking yet another allusion to the "Cape Feare" Simpsons episode, in which a Clinton picture figures.

It is also possible to know things unknowingly. One of the cleverest moments is when a newly arriving survivor is able to fill in missing elements of the "Cape Feare" dialogue and the trio of three little maids from The Mikado, even though he admits he has never seen a whole episode of The Simpsons. One line had been drilled into his mind by a girlfriend annoyingly obsessed with the series, and he assimilated Gilbert and Sullivan through membership of a light operatic society.

That conversation shows a sophisticated understanding of how the diffusion of themes and ideas works. I remember an Irish writer at a literary festival once quoting the comment of a Dublin taxi driver on a Taoiseach of the time – "to be sure, he has a picture in the attic" – as evidence that even a hired driver in the city had read Oscar Wilde's A Portrait of Dorian Gray. But, while Ireland would be a candidate for the nation with the most-literate population, it was equally possible that the cabbie had picked up the image of the artistic deal with the devil from everyday discourse, into which Wilde's story had long ago passed.

The Simpsons. Photograph: Allstar/Fox/Sportsphoto Ltd

And, while Washburn's detractors seem to have assumed that the author is endorsing a culture in which Bart is more significant than the Bard, she seems to me to be more neutrally presenting the way in which cultural history accrues through allusion, osmosis and confusion. The production (director Robert Icke, designer Tom Scutt) includes a tremendous visual gag in which, in the climatic musical performance, the spiky hairdo of Lisa Simpson has become blurred in the visual memory with the barbed helmet of the Statue of Liberty.

In that respect, the play is subject to a final irony. In the published text of Mr Burns (Oberon Books), there are two places where stage directions – "Microbeat of Maria doubt" and "She might be near tears at this point" – have accidentally been printed as dialogue. This raises the possibility that, in future productions of the text without the author present, an actor may, in a version of the transcription errors with which Shakespeare's plays are thought to be littered, speak these puzzling lines, perhaps delivering them as knowing Brechtian asides to the audience. As a result, Mr Burns itself could suffer the sort of cultural mistransmission that is its subject.

And, according to Aristotle, the protagonist of the lost poem by the author of the Iliad and the Odyssey was "an uncommonly dumb man". As, indeed, is the hero of a popular TV comedy 28 centuries later. So Homer's Margites and Marge's Homer have more in common than we thought, but, if Washburn's pessimism about electricity is correct, may one day both be known only through flickering reminiscence.